214 
POPULAR SCIENCE REVIEW. 
sion, which could, therefore, he made of silk. The movable coil is at the- 
centre of a rod carrying at the top a mercury cup, and dipping into another 
by its lower point. Both these were kept cool by a free circulation oi 
water, as in the “ tuyeres ” of a blast furnace. No difficulty from heating 
was experienced even with currents of 80 Webers. The resistances were 
large bands of German silver of the value of l-10th of an Ohm. 
With this apparatus the Wilde, Gramme, and Siemens machines were 
compared, with the result of placing the Gramme first, the Siemens second,, 
and the Wilde third in efficiency, although theoretically the Siemens should 
give the best result ; but it suffered the disadvantage in these experiments of' 
being run at a less speed than the others. 
Absolute Pitch . — An ingenious method for determining this was recently 
brought before the Musical Association by Lord Rayleigh. It depends on 
the principle that the absolute frequencies of vibration of two musical notes 
can be deduced from the interval between them, i.e., the ratio of their fre- 
quencies, and the number of beats which they occasion in a given time when 
sounded together. For example, if x and y denote the frequencies of two 
notes whose interval is an equal temperament major third, we know that 
y — l*25992.r. At the same time the number of beats heard in a second,, 
depending on the deviation of the third from true intonation, is 4 y - 5x. In. 
the harmonium these beats are readily counted with the aid of a resonator 
tuned to the common overtone, and thus are obtained two equations, from 
which the absolute values of x and y may be found by the simplest arith- 
metic. 
This method is not, however, practical in the case of the harmonium, 
in consequence of the pitch not being sufficiently constant, even when the 
blowing is carefully conducted with the aid of a pressure-gauge, the 
slightest change of interval being fatal to success. 
It is, therefore, necessary to be able to check the accuracy of the interval 
supposed to be known, at the same time that the beats are being counted. 
The equal temperament whole tone is intermediate between the minor 
and the major tone, lying nearer to the latter. Regarded as a disturbed 
major tone, it gives slow and, as a minor, comparatively quick beats. Both 
can be heard at the same time, and, when counted, give the means of calcu- 
lating the absolute pitch of both notes. If x and y be the frequencies of the 
notes, a and b those of the slow and quick beats — 
9 x — 8 y = a 
9 y — l(Xr = b 
whence 
x = 9a + 86 
y = 10a + 9 b 
This method in no way assumes the truth of the equal temperament 
whole tone. Four experiments are given in detail. The author believes 
that very accurate results might be obtained by the introduction of certain 
modifications. It is, however, impossible for one observer to count both 
sets of beats at the same time, or even one, without the aid of resonators. 
Further attempts at accuracy would be useless, for the cause above named, 
unless the comparison with a tuning-fork were simultaneous with the other 
observations ; and more observers would thus be required. 
